How can I make an animation of mesh pieces assembling (something like an explode modifier in reverse)?
Precondition
For this approach you will need the tiles as separate meshes (it doesn't appear to be your case).
To make an object into separate pieces (if they are already disconnected, but part of the same object), in Edit mode: select all the vertices (A), then P &gt; &quot;By loose parts&quot;. It's convenient to also select all the new meshes (that now share the same origin point) and do Object &gt; Origin &gt; Origin to center of mass.

Simple keyframed animation with a randomized starting point

Place your tiles in their final position.
Go to the last frame of the animation, select all the tiles, set a keyframe (I &gt; &quot;Location&quot;)


Go to the first frame.
Move the object to their average starting position behind the camera.


Hit Space for search (F3 in Blender 2.80), search &quot;Randomize Transform&quot;.
In the tool parameters, adjust the &quot;Location&quot; values, especially along the direction parallel to the camera orientation.
Add a new keyframe (I &gt; &quot;Location&quot;)


Done! Final result seen from the camera: